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(8x-5)(3x-6)=0
We multiply parentheses ..
(+24x^2-48x-15x+30)=0
We get rid of parentheses
24x^2-48x-15x+30=0
We add all the numbers together, and all the variables
24x^2-63x+30=0
a = 24; b = -63; c = +30;
Δ = b2-4ac
Δ = -632-4·24·30
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-33}{2*24}=\frac{30}{48} =5/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+33}{2*24}=\frac{96}{48} =2 $
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